Question

Suppose a sample of 941 floppy disks is drawn. Of these disks, 122 were defective. Using the data, construct the 95% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

Answer 1

Solution :

Given that,

n = 941

x = 122

= x / n = 122 / 941 = 0.130

1 - = 1 - 0.130 = 0.870

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.130 * 0.870) / 941)

= 0.022

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.130 - 0.022 < p < 0.130 + 0.022

0.108 < p < 0.152

(0.108 , 0.152)